Fuzzy Multicriteria Decision-Making Model Based on Z Numbers for the Evaluation of Information Technology for Order Picking in Warehouses

Abstract

Order-picking process management is one of the most demanding tasks within the operations of a warehouse system. It is especially evident in companies that have a high intensity of product flows, so the question of increasing the productivity of order picking arises. In this paper, a novel integrated fuzzy MCDM (Multicriteria Decision-Making) model was developed for the evaluation and selection of information technologies for order picking in a warehouse system, which is one of the most important novelties and contributions of the paper. Barcode, pick-to-light, pick-to-voice, and pick-to-vision technologies were evaluated based on IMF SWARA (improved fuzzy stepwise weight assessment ratio analysis) and fuzzy EDAS (evaluation based on distance from average solution) based on Z numbers. IMF SWARA-Z was applied to determine the importance of four criteria while the information technologies for order picking were evaluated with the fuzzy EDAS-Z method. The averaging of the estimates of the critera and alternatives was performed using the fuzzy Dombi aggregator. The results show that in this particular case under these research conditions, pick-to-vision is the best order-picking technology. Subsequently, validation tests were carried out, and they included the simulation of criteria weights and the impact of the reverse rank matrix.

1. Introduction

Conditioned by global requirements and frequent uncertainties, on the one hand, the modern market is characterized, first of all, by the great competition of business entities for the placement of their goods or services. On the other hand, such a market requires a constant minimization of the costs of all elements of business and an increase in the quality of products and services in order to be able to position themselves in the modern market. In particular, flexibility and reliability are highlighted, and they are among the most important factors in responding to global crises and the uncertainty of the entire supply chain. Logistics have proven to be very flexible and reliable under such circumstances. Within logistics subsystems, storage as a temporal transformation of material goods is an extremely important subsystem. This was particularly evident in recent years when the global crisis caused by various factors entered the scene. In such conditions, storage has become an essential logistical component in supply chains, by which it is possible to achieve competitiveness, enabling users’ requirements to be met in a way that allows an easier flow of goods to users and greater adaptability in meeting users’ requirements. This is reflected in an increased readiness for delivery, shortened delivery time, greater delivery reliability, etc. that the user expects from the supplier of goods, and, at the same time, reduces the total costs of logistics. Such requirements set for storage systems significantly complicate their structure and functioning above all the processes that are carried out in the warehouse [1]. Storage location and order-picking process represent two interrelated procedures that appear in storage systems that need to be solved independently as stated in [2]. Within warehouse systems, the order-picking process represents an extremely important and indispensable component that contributes to a large extent to the overall efficiency of the warehouse. This is confirmed by the fact that the order-picking process is the most resource-intensive process in a warehouse [3], which is largely influenced by the storage location policy applied. Order picking is an activity that significantly defines the quality of service the warehouse provides to users, which in modern business conditions, has special importance. This paper defines a model that deals with the issue of order picking with the aim of increasing the productivity of order pickers. Order picking, as the most common form of handling goods in warehouses, represents the formation of a set of different items that fulfill a certain need. Order-picking costs are often over 50% of the total operating costs of the warehouse while at the same time, 60% of the labor engagement in the warehouse belongs to these processes.

Numerous studies [4,5,6] have proven that the implementation of order-picking technology significantly affects business efficiency, enables cost reduction, and improves competitive advantage in the market. Today industrial processes need automation for an efficient and well-designed control system while soft computing approaches are most often used in these terms, as shown in [7]. This is one of the motivations and justifications for developing soft tools in our paper.

The aim of this paper from a professional aspect is to evaluate order-picking technologies in order to increase the productivity of the activities performed in warehouse systems. The criteria that will be applied to the selection of the order-picking technology are the possibility of implementing the technology, the costs of implementing the technology, and the possibility of improving its own performance and reliability.

The goals and contributions from the scientific level refer to the formation of a novel integrated fuzzy MCDM model. For the first time in the literature, a modification of the IMF SWARA and fuzzy EDAS methods using Z numbers is presented. In this way, it has made a contribution to the field that considers MCDM problems. This original model enables decision makers to make a more precise, mutual assessment of criteria and potential solutions. This consequently influences the final decision, which should be optimal.

Often, decisionmakers have doubts about which assessment to give when evaluating criteria or alternatives, so they often use interval fuzzy numbers [8,9], D numbers [10,11], or Z numbers, as we did in this paper. Z numbers enable more precise input data, which is one of the most important tasks in the decision-making process. More about the characteristics of Z numbers can be seen in Section 2 of this paper.

The short structure of the rest of the paper includes a procedure presentation of the methodology developed: Z numbers, main operations with these numbers, IMF SWARA method, fuzzy EDAS, and fuzzy Dombi aggregator are explained in Section 2. Section 3 contains a description of order-picking technologies and the formation of the MCDM model. In this section of the paper, the advantages and disadvantages of each alternative are given, and the criteria based on which it is necessary to select the best order-picking technology are described. Section 4 consists of the results with a presentation of the main steps of the methodology developed while in Section 5, validation tests are carried out. The final section provides a brief description of concluding considerations along with limitations and guidelines for further research.

2. Methods

2.1. Z Numbers

Z numbers were used for the modification, and thus their description is given below. Z numbers are a type of fuzzy number, i.e., two fuzzy numbers, related in a specific way. A Z number is an extension of a classic fuzzy number, providing greater opportunities to deal with additional uncertainties after decisions are made. The Z number concept was established by Zadeh [12]. The application of Z numbers in uncertain environments has already been presented in detail by Kang et al. [13]. Later, Z numbers have been applied with different MCDM methods by some authors [14,15,16].

Z numbers are an ordered pair of fuzzy numbers Z = ($\tilde{A}$, $\tilde{B}$). Fuzzy number $\tilde{A}$ is the first component representing the fuzzy limit of a certain variable X while fuzzy number $\tilde{B}$ is the second component representing the reliability of the first component ($\tilde{A}$). Figure 1 shows the form of a Z number with triangular fuzzy numbers [12].

A general notation of triangular Z numbers can be shown as:

$$\tilde{Z}=\left\{\left(a_1,a_2,a_3;w_{\tilde{A}}\right),(b_1,b_2,b_3;w_{\tilde{B}})\right\}$$

(1)

where the values $w_{\tilde{A}}$ and $w_{\tilde{B}}$ are weight factors of fuzzy number $\tilde{A}$ referring to $\tilde{B}$, which is, for the initial Z number, defined by most authors as $w_{\tilde{A}}=w_{\tilde{B}}=1$, $w_{\tilde{A}},w_{\tilde{B}}\in \left[0,1\right]$ ($w_{\tilde{A}}$ represents the height of generalized fuzzy number and $0\le w_{\tilde{A}}\le 1$) [17]. With the proof shown, the Z number is transformed into a classic fuzzy number in the following way:

Transforming the second part ($\tilde{B}$) into a crisp number by applying the centered method:

$$\alpha =\frac{a_1+a_2+a_3}{3}$$

(2)

The, add the weight of the second part ($\tilde{B}$) to the first part ($\tilde{A}$). The weighted Z number is shown as follows:

$${\tilde{Z}}^{\alpha }=\left\{\langle x,{\mu }_{{\tilde{A}}^{\alpha }}(x)\rangle |{\mu }_{{\tilde{A}}^{\alpha }}(x)=\alpha {\mu }_{\tilde{A}}(x)\right\}$$

(3)

which is given as:

$${\tilde{Z}}^{\alpha }=(a_1,a_2,a_3;\alpha )$$

(4)

Transform the weighted Z number into a regular fuzzy number. The regular fuzzy set is shown as follows:

$${\tilde{Z}}^{\prime }=\sqrt{\alpha }\ast \tilde{A}=(\sqrt{\alpha }\ast a_1,\sqrt{\alpha }\ast a_2,\sqrt{\alpha }\ast a_3)$$

(5)

2.2. IMF SWARA Method

The original SWARA method has been represented in the literature by Keršuliene et al. [18]. In meantime, many forms of the SWARA method [19] have been presented in the literature as a combination of intuitionistic fuzzy numbers [20], rough numbers [21], etc. We have used the IMF SWARA method to extend with the Z numbers because the fuzzy SWARA method in combination with Chang’s scale is not appropriate, as has been proven in [22].

The IMF SWARA method was proposed by Vrtagić et al. [23], and it contains the steps given below [24]:

Step 1: Put the criteria in descending order according to their expected importance.

Step 2: Identify relatively lower importance of the criterion (criterion Cj) in relation to the previous one (Cj − 1) and repeat it for each subsequent criterion. $\overline{{\wp }_j}$ represents the comparative importance of an average value.

Step 3: Define the fuzzy coefficient $\overline{{\Im }_j}$:

$$\overline{{\Im }_j}=\{\begin{array}{l}\overline{1}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}j=1\\ \overline{{\wp }_j}\oplus \overline{1}\hspace{1em}\hspace{1em}j>1\end{array}$$

(6)

Step 4: Define the obtained weights $\overline{{\aleph }_j}$:

$$\overline{{\aleph }_j}=\{\begin{array}{l}\overline{1}\hspace{1em}\hspace{1em}\hspace{1em}j=1\\ \frac{\overline{{\aleph }_{j-1}}}{\overline{{\Im }_j}}\hspace{1em}\hspace{1em}j>1\end{array}$$

(7)

$\overline{{\Im }_j}$ represents the fuzzy coefficient given in the previous step.

Step 5: Compute the fuzzy weight coefficients, Equation (9):

$$\overline{w_j}=\frac{\overline{{\aleph }_j}}{{\displaystyle \sum _{j=1}^n\overline{{\aleph }_j}}}$$

(8)

where the fuzzy relative weight of the criteria j is denoted by $\overline{w_j}$, and the number of criteria is denoted by n.

2.3. Fuzzy EDAS Method

The fuzzy EDAS method is carried out through the following steps [25,26]:

Step 1: Create an average decision matrix (X):

$$X={\left[{\overline{x}}_{ij}\right]}_{nxm}$$

(9)

$${\overline{x}}_{ij}=\frac{1}{k}{\oplus }_{p=1}^k{\overline{x}}_{ij}^p$$

(10)

where ${\overline{x}}_{ij}^p$ represents the performance value of alternative $A_i=\left(1\le i\le n\right)$ regarding criterion $c_j=\left(1\le j\le m\right)$ which is assigned by the pth decisionmaker $\left(1\le p\le k\right)$.

Step 2: Originally, in this step, criterion weights are created by averaging experts’ preferences. In this research, the IMF SWARA-Z method has been applied.

Step 3: Create an average solution matrix.

$$AV={\left[{\overline{av}}_j\right]}_{1\times m}$$

(11)

$${\overline{av}}_j=\frac{1}{n}\underset{i=1}{\overset{n}{\oplus }}{\overline{x}}_{ij}$$

(12)

where ${\overline{av}}_j$ is the average solutions regarding each criterion.

Step 4: Obtain a positive distance from average (PDA) and negative distance from average (NDA) solution. They should be obtained in accordance with a criterion type:

$$PDA={\left[{\overline{pda}}_{ij}\right]}_{n\times m}\Rightarrow {\overline{pda}}_{ij}=\{\begin{array}{l}\frac{\psi \left({\overline{x}}_{ij}-{\overline{av}}_j\right)}{k\left({\overline{av}}_j\right)}\hspace{1em}if\hspace{1em}j\in B\\ \frac{\psi \left({\overline{av}}_j-{\overline{x}}_{ij}\right)}{k\left({\overline{av}}_j\right)}\hspace{1em}if\hspace{1em}j\in C\end{array}$$

(13)

$$NDA={\left[{\overline{nda}}_{ij}\right]}_{n\times m}\Rightarrow {\overline{nda}}_{ij}=\{\begin{array}{l}\frac{\psi \left({\overline{av}}_j-{\overline{x}}_{ij}\right)}{k\left({\overline{av}}_j\right)}\hspace{1em}if\hspace{1em}j\in B\\ \frac{\psi \left({\overline{x}}_{ij}-{\overline{av}}_j\right)}{k\left({\overline{av}}_j\right)}\hspace{1em}if\hspace{1em}j\in C\end{array}$$

(14)

Step 5: Get the weighted sum of positive and negative distances for all alternatives:

$${\overline{sp}}_i=\underset{i=1}{\overset{m}{\oplus }}\left({\overline{w}}_j\otimes {\overline{pda}}_{ij}\right)$$

(15)

$${\overline{sn}}_i=\underset{i=1}{\overset{m}{\oplus }}\left({\overline{w}}_j\otimes {\overline{nda}}_{ij}\right)$$

(16)

Step 6: Normalize ${\overline{sp}}_i$ and ${\overline{sn}}_i$ values for all alternatives.

$${\overline{nsp}}_i=\frac{{\overline{sp}}_i}{\max \left(k\left({\overline{sp}}_i\right)\right)}$$

(17)

$${\overline{nsn}}_i=\frac{{\overline{sn}}_i}{\max \left(k\left({\overline{sn}}_i\right)\right)}$$

(18)

Step 7: Define the appraisal score (${\widetilde{as}}_i$) for all alternatives.

$${\overline{as}}_i=\frac{1}{2}\left({\overline{nsp}}_i\otimes {\overline{nsn}}_i\right)$$

(19)

Step 8: Rank the alternatives by decreasing values.

2.4. Fuzzy Dombi Agreggator

The fuzzy Dombi aggregator is presented by the following equations [24,27]:

$$FDWGA\left(\overline{\wp }\right)=\left({\wp }_j^l,{\wp }_j^m,{\wp }_j^u\right)=\{\begin{array}{l}{\wp }_j^l=\frac{{\displaystyle \sum _{j=1}^n\left({\wp }_j^l\right)}}{1+{\left\{{\displaystyle \sum _{j=1}^n{w}_j}{\left(\frac{1-f\left({\wp }_j^l\right)}{f\left({\wp }_j^l\right)}\right)}^{\rho }\right\}}^{1/\rho }}\\ {\wp }_{ij}^m=\frac{{\displaystyle \sum _{j=1}^n\left({\wp }_j^m\right)}}{1+{\left\{{\displaystyle \sum _{j=1}^n{w}_j}{\left(\frac{1-f\left({\wp }_j^m\right)}{f\left({\wp }_j^m\right)}\right)}^{\rho }\right\}}^{1/\rho }}\\ {\wp }_{ij}^u=\frac{{\displaystyle \sum _{j=1}^n\left({\wp }_j^u\right)}}{1+{\left\{{\displaystyle \sum _{j=1}^n{w}_j}{\left(\frac{1-f\left({\wp }_j^u\right)}{f\left({\wp }_j^u\right)}\right)}^{\rho }\right\}}^{1/\rho }}\end{array}$$

(20)

where the weights of s decisionmakers that participate in the research are denoted by w_j, p ≥ 0 represents a non-negative number, ${\wp }_j^l$ is a low value of TFN, ${\wp }_j^m$ is a middle value of TFN, and ${\wp }_j^u$ is an upper value of TFN.

$$f\left({\wp }_j^l,{\wp }_j^m,{\wp }_j^u\right)=\{\begin{array}{l}f\left({\wp }_j^l\right)=\frac{\left({\wp }_j^l\right)}{{\displaystyle \sum _{j=1}^n\left({\wp }_j^l\right)}}\\ f\left({\wp }_j^m\right)=\frac{\left({\wp }_j^m\right)}{{\displaystyle \sum _{j=1}^n\left({\wp }_j^m\right)}}\\ f\left({\wp }_j^u\right)=\frac{\left({\wp }_j^u\right)}{{\displaystyle \sum _{j=1}^n\left({\wp }_j^u\right)}}\end{array}$$

(21)

3. Description of Information Technologies for Order Picking and Formation of an MCDM Model

3.1. Order Picking

Order picking is a process of preparing goods for shipping according to the user’s order. In essence, it implies an individual or a combination of processes that are reflected through the joining, separating, and sorting of items. The order-picking process is the most common form of handling goods in warehouse systems, where it creates a set of different products that fulfills a certain demand, i.e., completes the delivery of goods by a predefined and necessary structure. Most frequently, the order-picking process is carried out at the warehouse exit, which ensures the delivery of the required range of products in a relatively short period of time. The quantity of each product differs from the contents of its storage unit. When it comes to the goods distribution subsystem, order picking appears as a point of transformation of the appearance of the goods in the warehouse into the appearance required by the user, and it refers to the classification of the goods and their quantity. Although order picking is only part of the goods handling operation in a warehouse, its importance is highly significant [2]. Order-picking costs are often over 50% of the total operating costs of a warehouse while at the same time, 60% of the labor engagement in the warehouse belongs to these processes.

3.2. Order-Picking Technologies

There is no doubt that technology will continue to evolve, and according to Fillip 2021 [28], it will impact human quality of life and other activities. Order-picking technologies that will be shown and evaluated in the MCDM model are as follows: Wireless order picking by barcode scanning (wireless picking system); Order picking by light detection (pick-to-light); Order picking by voice recognition (pick-to-voice); Vision order picking (pick-by-vision).

3.2.1. Wireless Picking System—Barcode Technology

This technology is one of the most commonly used in the field of logistics [29]. Barcode scanning equipment is cheaper than voice recognition terminals and can read information faster and more accurately than a human can read and talk. It is recommended that barcode scanning be used in systems that are too small to justify the installation and equipment costs for pick-to-light or pick-to-voice order picking as well as in systems where a large amount of information must be collected with each transaction [30].

The order picker uses a wireless handheld device (Figure 2) whereby:

• Based on the list of purchase orders from the central computer, a barcode label is generated, which is placed on a transport container for individual supplies.
• The empty container is transported by belt or roller conveyor to the order-picking section.
• The order picker scans the barcode on the container for individual supply with a wireless handheld device, and a list corresponding to the ordered content (list and quantity of ordered items) appears on the device.
• Based on the generated list, the order picker searches for and takes the ordered items by scanning the barcode of the tags on the items.
• After completing the order, the order picker enters the number of the products that make up the purchase order for the purpose of confirming the delivery.

The disadvantage of the wireless picking system is that one hand of the order picker is occupied, which makes it difficult for them to take items from shelves, which has been overcome by the application of advanced forms of this technology where both hands can be used. There are also problems when scanning barcode tags of nonstandard sizes, dirty tags, or in places where there is poor lighting.

There are also handheld devices that provide the order picker to use the hand on which the device is located to a certain extent for handling the material since part of the scanning device is placed on the finger, and the part with the display and keyboard is fixed on the forearm. With such a device, the order picker approaches and takes items from shelves more comfortably.

3.2.2. Pick-to-Light Technology

This technology is the best in systems where a high speed of order picking is required, and those are most often in the retail, pharmaceutical, cosmetic, and electronic industries. Since there is no reading, writing, or searching for items with this technology, it is ideal for systems with large amounts of data and items. Order picking time is reduced by up to 50%, and accuracy can be increased by more than 80%. These systems use small lights mounted on carriers on racks and are directed straight toward order pickers. When an order is received from the information system, the lights associated with the items on the list turn on. In addition to the lights, the display also shows the number of pieces of a particular item for the order. The order picker takes the required number of items and presses the button when the light turns off and approaches the next item where the light turns on. [32]

Pick-to-light systems are easy to be trained for and used and are ideal for large volumes of items. Figure 3 shows order picking by light detection.

In a cramped environment with a high speed of movement of items, a pick-to-light system enables successful task implementation because all lights associated with items for a specific order are turned on at the same time. In this way, the order picker can determine the best order for taking individual items, which leads to a higher speed of order picking.

The pick-to-light system requires the order picker to respond to light signals that identify the location and number of items to be taken from a shelf. When taking the required number of an item is completed, the order picker presses a button, turning it off and confirming that the process has been finished. Compared to others, this technology enables the highest order-picking speed. However, the system is not flexible, as it requires a fixed installation of equipment that cannot be moved so easily. Costs increase with each new item.

3.2.3. Pick-to-Voice Technology

Pick-to-voice technology implies two-way communication between the order picker and the management system [5]. Employees receive voice instructions from the control system and respond verbally using headphones and microphones connected to a control unit carried by the worker on his belt [34]. Order picking by voice recognition is shown in Figure 4.

Order picking by voice recognition (pick-to-voice) is done in the following way:

• The central computer receives a work order from the control system and these instructions are transformed into voice commands that are placed by priority in a series of tasks for order picking.
• The order picker receives verbal instructions through headphones to go and collect the first item from the order.
• The order picker confirms the location of the item by reading the address from the shelf. If the address matches the expected response, the system further instructs the order picker on how many items to pick up. The order picker confirms the pickup by repeating the number.
• If the location on the shelf is empty or the number of items is less than the number required, the order picker reports that, and the system generates an order to fill in the location.
• When each operation is completed, the system gives instructions for the next work order.
• If the order picker does not hear or does not understand the command, they can request the command be repeated.
• According to the experiences of users of this technology, the training time of order pickers is reduced from a few days to a few hours.

The voice recognition system is particularly effective where it is not necessary to have both hands free to handle items. Voice recognition is mostly used for ordering, but the technology is also applicable for other activities, such as goods receiving, storage, replenishment, sorting, and loading. The advantages of this technology are fewer order picking errors, increased productivity, reduced number of complaints, and shortened training time for order pickers.

3.2.4. Pick-to-Vision Technology

Pick-to-vision technology represents a new concept in storage systems made possible by using smart glasses, which transmit information from the server directly to the observer’s field of vision via WLAN technology. Through the barcode scanner, when the warehouse worker receives the product, his glasses will light up green if it is the right item or red if it is the wrong product.

Smart glasses can also be used to determine the position of an observer in a warehouse. Based on this, they can be used to manage the virtual warehouse using graphic symbols that lead an employee to a specific location, see Figure 5.

The paper [37] presents certain conclusions about the application of smart glasses in the field of logistics and order picking in warehouse systems. The conclusions state that the use of this technology affects walking performance in terms of the risk of slipping or falling. Then, workers point out that the glasses are too heavy and sometimes uncomfortable to wear, and their adjustment can be difficult. Moreover, in certain situations, there are problems related to fitting the glasses because the entire field of vision is not available. Another problem of a technical nature implies that the glasses lose their orientation, so the order picker has to move a few steps backward in order to be able to identify the objects that are in front of him. There are numerous advantages to applying this technology, but it still requires configuration improvement, especially in terms of ergonomics [37].

3.3. Formation of an MCDM Model

The criteria that were necessary for determining the weights that were applied in the IMF SWARA-Z method were the possibility of implementation (C1), technology implementation costs (C2), performance improvement possibility (C3), and technology reliability (C4).

The technologies used to evaluate potential solutions applying the fuzzy EDAS-Z method with averaging with the fuzzy Dombi aggregator were wireless picking using barcode scanning (wireless picking system)—A1, order picking by light detection (pick-to-light)—A2, order picking by voice recognition (pick-to-voice)—A3, vision order picking (pick-to-vision)—A4.

Wireless order picking using barcode scanning (wireless picking system) involves scanning items based on a previously generated list received from a central computer. After completing the order, the order picker enters the number of the products that make up the order to confirm the delivery.

Order picking by light detection (pick-to-light) uses small lights mounted on carriers on racks and are directed straight toward order pickers. When an order is received from IS, the lights associated with the listed items are turned on. Besides the lights, the display also shows the number of pieces of a particular item for the order. The order picker takes the required number of items and presses the button when the light turns off and approaches the next item where the light is on. Order picking by voice recognition (pick-to-voice) implies two-way communication between the order picker and the management system. Employees receive voice instructions from the control system and respond verbally using headphones and microphones connected to a control unit carried by a worker on his belt. The pick-to-vision technology represents a new concept in storage systems, which is made possible by using smart glasses, which transmit information from the server directly to the observer’s field of vision via WLAN technology.

4. Results

4.1. Determining the Weights of the Criteria—IMF SWARA-Z

In this section of the research, the procedure for determining the importance of criteria for the evaluation of information technology for order picking is presented. The evaluation was performed on the basis of the defined scale shown in

Table 1. Linguistics and the TFN scale.

Linguistic Variable	TFN A	Linguistic Variable	TFN B
Absolutely less significant—ALS	(1, 1, 1)	Very small (VS)	(0, 0, 0.2)
Dominantly less significant—DLS	(1/2, 2/3, 1)	Small (S)	(0.1, 0.25, 0.4)
Much less significant—MLS	(2/5, 1/2, 2/3)	Medium (M)	(0.3, 0.5, 0.7)
Really less significant—RLS	(1/3, 2/5, 1/2)	High (H)	(0.55, 0.75, 0.95)
Less significant—LS	(2/7, 1/3, 2/5)	Very high (VH)	(0.8, 1, 1)
Moderately less significant—MDLS	(1/4, 2/7, 1/3)
Weakly less significant—WLS	(2/9, 1/4, 2/7)
Equally significant—ES	(0, 0, 0)

, which is used exclusively for the IMF SWARA-Z method.

Five DMs (experts) who were chosen on the basis of their experience and skills in the field of warehouse process management and information technology evaluated the criteria, i.e., compared them mutually, which is shown in

Table 2. Intercomparison of criteria in the IMF SWARA-Z method by five DMs.

E1	A	B	E2	A	B	E3	A	B	E4	A	B	E5	A	B
C2			C2			C2			C2			C2
C4	ES	VH	C1	WLS	VH	C4	WLS	H	C4	MDLS	M	C4	ES	VH
C1	LS	M	C4	ES	VH	C1	MDLS	H	C3	ES	VH	C1	LS	VH
C3	MDLS	H	C3	WLS	M	C3	WLS	VH	C1	WLS	VH	C3	MDLS	VH

.

In Table 2, the symbol E denotes an expert, i.e., a decisionmaker, and A and B represent the TFN from the criterion evaluation scale. After the evaluation was presented using the scale for the IMF SWARA-Z method, it was necessary to perform the conversion into ordinary TFNs, which is shown in

Table 3. Evaluation of criteria after transformation of Z numbers into TFNs.

E1	$\overline{{\mathit{\wp }}_{\mathit{j}}}$	E2	$\overline{{\mathit{\wp }}_{\mathit{j}}}$	E3	$\overline{{\mathit{\wp }}_{\mathit{j}}}$	E4	$\overline{{\mathit{\wp }}_{\mathit{j}}}$	E5	$\overline{{\mathit{\wp }}_{\mathit{j}}}$
C2		C2		C2		C2		C2
C4	(0, 0, 0)	C1	(0.215, 0.242, 0.276)	C4	(0.192, 0.217, 0.247)	C4	(0.177, 0.202, 0.236)	C4	(0.215, 0.242, 0.276)
C1	(0.202, 0.236, 0.283)	C4	(0, 0, 0)	C1	(0.217, 0.247, 0.289)	C3	(0, 0, 0)	C1	(0.215,0.242,0.276)
C3	(0.217, 0.247, 0.289)	C3	(0.157, 0.177, 0.202)	C3	(0.215, 0.242, 0.276)	C1	(0.215, 0.242, 0.276)	C3	(0.215, 0.242, 0.276)

.

The IMF SWARA-Z method was applied for each model separately, i.e., one calculation model was created for each expert, and the results for E1 are shown in

Table 4. Calculation of criterion weights by IMF SWARA-Z method for E1.

E1	$\overline{{\mathit{\wp }}_{\mathit{j}}}$	$\overline{{\mathit{\Im }}_{\mathit{j}}}$	$\overline{{\mathit{\aleph }}_{\mathit{j}}}$	$\overline{{\mathit{w}}_{\mathit{j}}}$
C2		(1, 1, 1)	(1, 1, 1)	(0.284, 0.289, 0.295)
C4	(0, 0, 0)	(1, 1, 1)	(1, 1, 1)	(0.284, 0.289, 0.295)
C1	(0.202, 0.236, 0.283)	(1.202, 1.236, 1.283)	(0.78, 0.809, 0.832)	(0.222, 0.234, 0.246)
C3	(0.217, 0.247, 0.289)	(1.217, 1.247, 1.289)	(0.605, 0.649, 0.684)	(0.172, 0.188, 0.202)
			(3.384, 3.458, 3.516)

.

After calculating the IMF SWARA-Z method, the following weights were obtained for all expert estimates:

$$\begin{array}{l}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(E_1\right):\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(E_2\right):\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(E_3\right):\\ \overline{w_1}=\left(0.222,0.234,0.246\right),\hspace{1em}\overline{w_1}=\left(0.233,0.244,0.256\right),\hspace{1em}\overline{w_1}=\left(0.201,0.219,0.237\right)\\ \overline{w_2}=\left(0.284,0.289,0.295\right),\hspace{1em}\overline{w_2}=\left(0.298,0.303,0.311\right),\hspace{1em}\overline{w_2}=\left(0.323,0.332,0.343\right)\\ \overline{w_3}=\left(0.172,0.188,0.202\right),\hspace{1em}\overline{w_3}=\left(0.194,0.208,0.221\right),\hspace{1em}\overline{w_3}=\left(0.157,0.176,0.195\right)\\ \overline{w_4}=\left(0.284,0.289,0.295\right),\hspace{1em}\overline{w_4}=\left(0.233,0.244,0.256\right),\hspace{1em}\overline{w_4}=\left(0.259,0.273,0.288\right)\end{array}$$

$$\begin{array}{l}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(E_4\right):\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(E_5\right):\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\\ \overline{w_1}=\left(0.187,0.201,0.215\right),\hspace{1em}\overline{w_1}=\left(0.201,0.218,0.235\right)\\ \overline{w_2}=\left(0.294,0.300,0.307\right),\hspace{1em}\overline{w_2}=\left(0.327,0.336,0.347\right)\\ \overline{w_3}=\left(0.238,0.250,0.261\right),\hspace{1em}\overline{w_3}=\left(0.157,0.176,0.194\right)\\ \overline{w_4}=\left(0.238,0.250,0.261\right),\hspace{1em}\overline{w_4}=\left(0.256,0.271,0.286\right)\end{array}$$

Then the fuzzy Dombi aggregator was applied in order to average the weights of the criteria presented previously. An example of calculation for averaging is as follows:

$$FDWGA\left(\overline{w_1}\right)=\left(w_1^l,w_1^m,w_1^u\right)=\{\begin{array}{l}{w}_1^l=\frac{{\displaystyle \sum _{j=1}^n\left(w_j^l\right)}}{1+{\left\{{\displaystyle \sum _{j=1}^n{w^{\prime }}_j}{\left(\frac{1-f\left(w_j^l\right)}{f\left(w_j^l\right)}\right)}^{\rho }\right\}}^{1/\rho }}=\frac{1.043}{1+\left(0.2\times \frac{1-0.213}{0.213}\right)+\left(0.2\times \frac{1-0.223}{0.223}\right)+\left(0.2\times \frac{1-0.193}{0.193}\right)+\left(0.2\times \frac{1-0.179}{0.179}\right)+\left(0.2\times \frac{1-0.193}{0.193}\right)}=0.207\\ w_1^m=\frac{{\displaystyle \sum _{j=1}^n\left(w_j^m\right)}}{1+{\left\{{\displaystyle \sum _{j=1}^n{w^{\prime }}_j}{\left(\frac{1-f\left(w_j^m\right)}{f\left(w_j^m\right)}\right)}^{\rho }\right\}}^{1/\rho }}=\frac{1.116}{1+\left(0.2\times \frac{1-0.210}{0.210}\right)+\left(0.2\times \frac{1-0.218}{0.218}\right)+\left(0.2\times \frac{1-0.196}{0.196}\right)+\left(0.2\times \frac{1-0.180}{0.180}\right)+\left(0.2\times \frac{1-0.195}{0.195}\right)}=0.222\\ w_1^u=\frac{{\displaystyle \sum _{j=1}^n\left(w_j^u\right)}}{1+{\left\{{\displaystyle \sum _{j=1}^n{w^{\prime }}_j}{\left(\frac{1-f\left(w_j^u\right)}{f\left(w_j^u\right)}\right)}^{\rho }\right\}}^{1/\rho }}=\frac{1.189}{1+\left(0.2\times \frac{1-0.207}{0.207}\right)+\left(0.2\times \frac{1-0.215}{0.215}\right)+\left(0.2\times \frac{1-0.199}{0.199}\right)+\left(0.2\times \frac{1-0.181}{0.181}\right)+\left(0.2\times \frac{1-0.198}{0.198}\right)}=0.237\end{array}$$

The other values were obtained in the same way so that after the application of the IMF SWARA-Z and fuzzy Dombi aggregator, the final values of the weighting coefficients of the criteria were as follows:

$$\begin{array}{l}\overline{w_1}=\left(0.207,0.222,0.237\right)\\ \overline{w_2}=\left(0.304,0.311,0.320\right)\\ \overline{w_3}=\left(0.179,0.196,0.212\right)\hspace{1em}\\ \overline{w_4}=\left(0.253,0.264,0.276\right)\end{array}$$

4.2. Evaluation of Order Picking Technologies Using the Fuzzy EDAS-Z Method

After the previously determined importance of the criteria, further, in this section, the evaluation and selection of order-picking technologies in the warehouse system using the fuzzy EDAS-Z method is performed. First, a scale for evaluating potential solutions was created (

Table 5. Scale for evaluating order-picking technologies using the fuzzy EDAS-Z method.

Linguistic Variable	TFN A	Linguistic Variable	TFN B
Very low—VL	(0, 0, 1, 2)	Very small (VS)	(0, 0, 0.2)
Low—L	(1, 2, 2, 3)	Small (S)	(0.1, 0.25, 0.4)
Medium low—ML	(2, 3, 4, 5)	Medium (M)	(0.3, 0.5, 0.7)
Medium—M	(4, 5, 5, 6)	High (H)	(0.55, 0.75, 0.95)
Medium high—MH	(5, 6, 7, 8)	Very high (VH)	(0.8, 1, 1)
High—H	(7, 8, 8, 9)
Very high—VH	(8, 9, 10, 10)

). After which, the experts started evaluating the information technologies used for order picking, and the evaluation by all experts is shown in

Table 6. Evaluation of order-picking technologies.

E1

A1

A2

A3

A4

E2

A1

A2

A3

A4

A

B

A

B

A

B

A

B

A

B

A

B

A

B

A

B

C1

VH

H

H

VH

ML

VH

H

M

C1

H

VH

MH

VH

M

H

VH

M

C2

ML

H

M

H

H

H

VH

H

C2

M

VH

MH

H

VH

M

VH

H

C3

M

VH

MH

H

H

VH

H

H

C3

M

H

MH

H

H

VH

H

VH

C4

ML

H

MH

VH

H

VH

H

M

C4

ML

VH

H

M

H

H

VH

M

E3

A1

A2

A3

A4

E4

A1

A2

A3

A4

A

B

A

B

A

B

A

B

A

B

A

B

A

B

A

B

C1

VH

VH

H

H

M

VH

M

VH

C1

VH

VH

H

VH

M

VH

H

H

C2

M

VH

MH

VH

H

VH

VH

VH

C2

M

VH

M

VH

H

H

H

VH

C3

ML

H

MH

H

H

H

H

H

C3

H

H

H

H

VH

H

H

H

C4

M

VH

MH

VH

VH

H

VH

H

C4

M

VH

MH

VH

H

VH

H

H

E5

A1

A2

A3

A4

A

B

A

B

A

B

A

B

C1

VH

VH

H

VH

H

H

H

H

C2

H

VH

M

VH

H

VH

H

VH

C3

H

H

VH

H

H

H

VH

H

C4

M

VH

H

M

M

VH

H

H

.

In order to form the initial fuzzy decision matrix shown in

Table 7. Initial fuzzy EDAS-Z matrix.

	A1	A2	A3	A4
C1	(7.35, 8.3, 9, 9.24)	(6.13, 7.09, 7.35, 8.3)	(3.43, 4.5, 4.88, 5.86)	(5.17, 6.03, 6.14, 6.87)
C2	(3.33, 4.4, 4.81, 5.79)	(4.02, 4.95, 5.22, 6.16)	(6.23, 7.1, 7.26, 7.96)	(7, 7.93, 8.43, 8.86)
C3	(3.44, 4.5, 4.92, 5.87)	(4.99, 5.88, 6.63, 7.39)	(6.49, 7.4, 7.54, 8.3)	(6.35, 7.24, 7.38, 8.13)
C4	(2.67, 3.7, 4.28, 5.23)	(4.88, 5.74, 6.27, 7.12)	(5.79, 6.77, 6.89, 7.74)	(5.86, 6.66, 6.92, 7.46)

, it was necessary to first transform the Z numbers into TFNs, and then reapply the fuzzy Dombi aggregator, as already explained in the previous section of this paper.

Applying the methodology of the fuzzy EDAS method, i.e., Equations (9)–(19), the results presented in

Table 8. The results of order-picking technology selection using novel IMF SWARA-Z–fuzzy EDAS-Z model.

	$\widetilde{s{p}_i}$	$\widetilde{s{n}_i}$	$\widetilde{ns{p}_i}$
A1	(−0.01, 0.05, 0.09, 0.13)	(−0.07, 0.17, 0.27, 0.51)	(−0.05, 0.31, 0.55, 0.8)
A2	(−0.14, −0.01, 0.05, 0.2)	(−0.11, 0.03, 0.1, 0.23)	(−0.89, −0.05, 0.35, 1.27)
A3	(−0.13, 0.09, 0.15, 0.37)	(−0.01, 0.05, 0.08, 0.14)	(−0.81, 0.56, 0.97, 2.34)
A4	(−0.09, 0.12, 0.21, 0.39)	(−0.05, 0.01, 0.03, 0.08)	(−0.57, 0.77, 1.32, 2.51)
	$\widetilde{ns{n}_i}$	$\widetilde{a{s}_i}$	$\mathrm{k}(\widetilde{a{s}_{i)}}$	Rank
A1	(−1.3, −0.25, 0.23, 1.31)	(−0.67, 0.03, 0.39, 1.06)	0.199	4
A2	(−0.06, 0.56, 0.85, 1.52)	(−0.48, 0.26, 0.6, 1.4)	0.447	3
A3	(0.37, 0.64, 0.76, 1.05)	(−0.22, 0.6, 0.86, 1.7)	0.735	2
A4	(0.63, 0.87, 0.95, 1.21)	(0.03, 0.82, 1.13, 1.86)	0.958	1

were obtained. Since, by their nature, the IMF SWARA method and the fuzzy EDAS method use triangular and trapezoidal fuzzy numbers, respectively, in their algorithms, it is important to note that the defuzzified values obtained by applying the IMF SWARA-Z method were used while weighting the decision matrix in the fuzzy EDAS-Z model.t

The results obtained by using the IMF SWARA-Z–Fuzzy EDAS-Z model based on the fuzzy Dombi aggregator show that the ranking of alternatives is A4 > A3 > A2 > A1. The best order-picking technology is pick-to-vision, which was the last technology created and currently appears as a dominant technology in many systems as a result of its advantages which are described in the section related to order-picking technologies. The second most favorable technology is pick-to-voice (A3), which is better than the third-ranked, pick-to-light (A2), which is a consequence of much greater flexibility and investments compared to pick-to-voice and pick-to-light. The last position is barcode technology, which is used in storage systems with a low level of information technology implementation.

The costs of barcode scanning and the pick-to-voice system depend on the number of order pickers who use the system while the number of items does not have a significant impact on the cost. The reverse is the case with the pick-to-light system, where the number of order pickers does not significantly affect costs but the number of items does. The main advantage of pick-to-vision compared to pick-by-voice and pick-by-light systems is the display of all necessary information (position, item, and quantity) in the observer’s field of vision, which means faster information transfer.

5. Validation Tests

5.1. Sensitivity Analysis

In order to determine the sensitivity of changes in the results achieved, the influence of changes in the values of the criteria was tested. This was determined by a simulation through 40 scenarios in which the values of all four criteria were changed using Equation (22) [38,39]:

$$W_{n\beta }=\left(1-W_{n\alpha }\right)\frac{W_{\beta }}{\left(1-W_n\right)}$$

(22)

The first 10 scenarios implied a reduction of the first criterion in the range of 5–95% of its own value, S11–S20 implied a reduction of the second criterion, S21–S30 implied a reduction of the third criterion, and finally S31–S40 implied a reduction of the fourth criterion in the same specified interval. Figure 6 shows all simulated criterion weights in the 40 scenarios.

Values of criteria weights have been simulated as follows: in S1, the value of the first criterion was reduced by 5%; in the second, by 15; in the third, by 30%; and until scenario S10, in which the value was reduced by 95%. The new simulated weights in the mentioned scenarios were 0.211, 0.189, 0.167, 0.144, 0.122, 0.100, 0.078, 0.056, 0.033, and 0.011, respectively. In the same way, it was simulated that criteria weights in scenarios S21–S40 reduced the second, third, and fourth criteria, respectively. It should be noted that in parallel with a decrease in the value of a certain criterion, the values of the other criteria increased proportionally so that the sum of the weights remained the same.

After simulating the weights of the criteria, the recalculation for each of the 40 scenarios separately was started. The fuzzy EDAS-Z method was applied again in order to determine the sensitivity of the model to changes in the weights of the criteria, the results of which are shown in Figure 7.

As previously observed, the values of the evaluation results of order-picking technologies range from the worst with a value of 0.199 to the best with a value of 0.958. It can be concluded that there are two main reasons for retaining the initial ranking in all-new scenarios. The first has already been explained and refers to the large range in the values of alternatives, and the second implies a small set of criteria and alternatives, having a higher probability of model stability. In the sensitivity analysis carried out, the modified value of the criteria was, e.g., only 0.010 (C3 in S30), but still, there was no change in the ranks of the order-picking technologies; the rank in all scenarios was A4 > A3 > A2 > A1. It is confirmed that the best order-picking technology is pick-to-vision.

5.2. Impact of Reverse Rank Matrices

In addition to the previous analysis, an analysis of the dynamic influence of the initial matrix size was also conducted. It implied that the worst-ranked alternative was eliminated from the decision matrix and that the calculation was repeated. In this way, the worst alternatives were eliminated until one remained, and that the one represents the best solution. The results of the analysis of the changes in the initial matrix size are shown in Figure 8.

As can be noticed, if the initial matrix size was modified, the final values of the order-picking technologies changed, which was quite expected, while the ranking of the alternatives did not change in any case. This is an additional indicator of the stability of the proposed IMF SWARA-Z–Fuzzy EDAS-Z model.

6. Conclusions

Decision making is a specific form of activity [40], and many MCDM methods are used for numerous decision problems from different disciplines [41]. In order to implement measures in the area of warehouse systems to possibly increase productivity, a fuzzy MCDM model for the evaluation of order-picking technologies was defined. The greatest novelty and contribution of this paper is reflected in the fact that it formed a novel MCDM model employing the application of IMF SWARA and fuzzy EDAS methods based on Z numbers and the application of a fuzzy Dombi aggregator for averaging the initial group decision matrix. Order-picking technologies have been evaluated from the aspect of professional contribution, whereby the selected technology can greatly contribute to increasing the productivity of products picked in a unit of time. The results show that in the conditions and circumstances of this evaluation, the best order-picking technology is the application of smart glasses.

Limitations that can be defined refer to a relatively small set of parameters on the basis of which order-picking technologies were evaluated and the current circumstances under which the research was conducted. Guidelines for the continuation of this or similar research primarily depend on the conditions of the company that asked for the order-picking technology evaluation project. This refers to the consideration of only those parameters that are the focus of the requirements of a particular company.

Implementation of the best order-picking technology in a warehouse should be done next year. In addition, the possibility of implementing a rough set theory for group decision making can be an adequate basis for future decision making. Moreover, the assessment of other logistics activities can be the subject of future evaluation and consideration regarding the needs for creating the MCDM model in such a way that increases the efficiency of the whole business.